SAT

SAT Math Formulas You Need to Know (Beyond the Reference Sheet)

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The Digital SAT reference sheet covers mostly geometry: areas, volumes, the Pythagorean theorem and special right triangles. You still need to memorize formulas for slope and lines, quadratics and the discriminant, exponent rules and exponential growth, percent change, mean and median, circle equations, and basic trigonometry.

What the reference sheet includes

Memorizing these still helps, because it saves opening the sheet on every question.

  • Circle: area A = πr², circumference C = 2πr.
  • Rectangle: A = lw. Triangle: A = ½bh.
  • Pythagorean theorem: a² + b² = c².
  • Special right triangles: 30-60-90 (x, x√3, 2x) and 45-45-90 (s, s, s√2).
  • Volumes: rectangular prism lwh, cylinder πr²h, sphere (4/3)πr³, cone (1/3)πr²h, pyramid (1/3)lwh.
  • A circle has 360° or 2π radians, and the angles in a triangle add up to 180°.

Lines and systems of equations

  • Slope: m = (y₂ − y₁) / (x₂ − x₁).
  • Slope-intercept form: y = mx + b. Point-slope form: y − y₁ = m(x − x₁). Standard form Ax + By = C has slope −A/B.
  • Parallel lines have equal slopes; perpendicular slopes are negative reciprocals.
  • Systems: different slopes give one solution; same slope and different intercepts give no solution; the same line gives infinitely many solutions.

Quadratics

  • Standard form y = ax² + bx + c; vertex form y = a(x − h)² + k; factored form y = a(x − r)(x − s).
  • Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a.
  • Discriminant b² − 4ac: positive means two real solutions, zero means one, negative means none.
  • Vertex x-coordinate: x = −b / 2a. Sum of roots −b/a; product of roots c/a.

Exponents, growth and percentages

  • xᵃ · xᵇ = xᵃ⁺ᵇ, xᵃ / xᵇ = xᵃ⁻ᵇ, (xᵃ)ᵇ = xᵃᵇ, x⁰ = 1, x⁻ᵃ = 1/xᵃ.
  • Exponential growth or decay: y = a(1 ± r)ᵗ, where a is the starting amount and r is the rate as a decimal.
  • Percent change = (new − original) / original × 100.
  • Increase by p%: multiply by (1 + p/100). Decrease by p%: multiply by (1 − p/100).

Statistics and probability

  • Mean is the sum divided by the count; median is the middle value in order; range is maximum minus minimum.
  • Outliers pull the mean much more than the median.
  • Standard deviation measures spread: data close to the mean has a smaller standard deviation.
  • Probability = favorable outcomes ÷ total outcomes. In two-way tables, check which group the question describes.

Circles, triangles and trigonometry

  • Circle equation: (x − h)² + (y − k)² = r², center (h, k). Completing the square often puts it in this form.
  • Arc length = (angle/360°) × 2πr. Sector area = (angle/360°) × πr². 180° = π radians.
  • SOHCAHTOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent; sin(x) = cos(90° − x).
  • Similar triangles have proportional sides and equal angles.
  • Distance: √[(x₂ − x₁)² + (y₂ − y₁)²]. Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2).

Know when to use each formula

The SAT tests whether you can recognize which formula a word problem calls for and explain what each part means, such as the starting value or rate. After each question, ask what in the wording pointed to the formula, and use Desmos to check formula-based answers.

Sources

Frequently asked questions

Does the Digital SAT give you a formula sheet?

Yes. Bluebook includes a reference sheet with common geometry formulas, but it does not include formulas such as slope, the quadratic formula, exponent rules or the circle equation.

Which SAT math formulas should I memorize first?

Start with slope and linear equation forms, the quadratic formula and discriminant, exponential growth and percent change, because algebra and advanced math make up most of the Math section.

Is the quadratic formula on the SAT reference sheet?

No. You need to know it, though Desmos can also find the solutions of a quadratic by graphing it.

Still have a question? Talk to an advisor.